Elementary equation

idontknow

Given equation $$\displaystyle x=x^2$$ which has two real solutions 0 and 1.
Solve the equation using approximation (Newtonâ€™s method).
Can anyone post it in short-terms (also other approximations)?

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skipjack

Forum Staff
Newton-Raphson method: if $x$ is your first approximation (nearer to 0 or 1 than to 1/2), use $x^2/(2x - 1)$ as your next approximation.

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